Conservation, convergence, and computation for evolving heterogeneous elastic wires

The elastic energy of a bending-resistant interface depends both on its geometry and its material composition. We consider such a heterogeneous interface in the plane, modeled by a curve equipped with an additional density function. The resulting energy captures the complex interplay between curvature and density effects, resembling the Canham-Helfrich functional. We describe the curve by its inclination angle, so that the equilibrium equations reduce to an elliptic system of second order. After a brief variational discussion, we investigate the associated nonlocal $L^2$-gradient flow evolution, a coupled quasilinear parabolic problem. We analyze the (non)preservation of quantities such as convexity, positivity, and symmetry, as well as the asymptotic behavior of the system. The results are illustrated by numerical experiments.Comment: 34 pages, 13 figures. Comments are welcome

Modelling the characteristics of the baroreceptor

A dissertation submitted to the Faculty of Engineering and the Built Environment, University of Witwatersrand in fulfilment of the requirements for the degree of Master of Science in Engineering. 2017The baroreceptor is a stretch receptor which detects changes in pressure in arterial blood vessels. Baroreceptor nerves inform the brainstem of changes in blood pressure, which then influences sympathetic and parasympathetic nervous activity to counteract that change. Due to the relationship between essential hypertension, sympathetic nervous activity and the baroreflex, there is some debate in the literature about whether the baroreflex can act as a long-term controller of blood pressure. This debate has increased in recent years, due to the high prevalence of essential hypertension in all societies and the introduction of new technologies to counteract drug-resistance hypertension. The baroreflex has become a source of debate due to the complex physiological feedback control that regulates blood pressure and due to new stimulating electrical devices, which have shown promising results in reducing drug-resistant essential hypertension. system. This is done through a literature survey extending through experimental and modelling research, where selected mathematical models of the baroreceptor are then analysed and simulated to find the best performing model, so that they may be simulated for an extended frequency response than what would be experimentally possible. The purpose of this investigation is to determine, through simulation, what the sensor static and dynamic characteristics are. Through this characterisation of the sensor behaviour of the baroreceptor in the baroreflex control loop, it is then possible to infer whether the baroreflex can act as a long-term controller of blood pressure. An overview of experimental and analytical investigations on the baroreceptor over the last 70 years is summarised. This overview includes mathematical models, which predict experimental results. A subset of four models from Srinivasen et al., Bugenhagen et al., Beard et al. and Mahdi et al. are selected. These models are implemented in MATLAB and Simulink. The parameters and experimental conditions are integrated into the Simulink models, and the simulated results are compared to the reported experimental data. In this way, each mathematical model is evaluated using secondary data for its ability to simulate the expected behaviour. Thereafter, all simulated models are compared under the same input conditions (a 0-230 mmHg step input over 12 s). These results are used to select the best performing models, based on how well they were parameterised and validated for experimental tests. The best performing models are those of Beard et al. and Bugenhagen et al. They are tested for a wide range of artificial inputs at different frequencies, with sinusoidal inputs which have periods that range from 0.1 s to 10 days and have a 100 mmHg operating point with a 1 mmHg peak amplitude. All modelling techniques studied show that the baroreceptor firing response resets due to the rate of change in strain in the visco-elastic arterial wall. Both tested model frequency responses, although parameterised for different species and for different major vessels, show high sensitivity to inputs in range from 1 s to 1 min 36 s (0.01 Hz 1Hz), and very low sensitivity for changes that are longer than 16 min 36s (0.001 Hz). This extrapolated simulation suggests a zero gain near DC. The simulated frequency response of the best performing baroreceptor models, which were validated against short-term experimental data, indicate that the baroreceptor is only able to sense changes that happen in less than 1 min 16s. The critical analysis of all the simulated baroreceptor models show that this characteristic of the baroreceptor is caused by the visco-elastic layers of the arterial wall, and is likely in all baroreceptors regardless of type or species. It also indicates that under electrical stimulation of the baroreceptor, the input signal from the electrical device bypasses the baroreceptor nerve ending (which is embedded in the arterial wall) and that the electrical signal of the baroreceptor is bypassed by the new stimulated electrical signal of the device. Furthermore, if the sensor can only detect short-term changes, then it is unlikely that the baroreceptor can inform the brainstem on longterm changes to mean arterial blood pressure. Therefore, based on the models examined in this study, this suggests that the baroreceptor is unlikely to be involved in long-term blood pressure control. This analysis of the best performing model is presented to show the limitations of the baroreflex in long term control of blood pressure. It serves as a simulated experiment to rationalise the contentious debate around the role of the baroreflex in long term blood pressure control, and to allow for future improvements that can be made on the baroreceptor model to allow for more extended modelling on sor characteristics. An improvement that could be applied to the best performing baroreceptor models, implemented in this study, is to examine the effects of ageing and inter-species variability on carotid sinus dimensions and visco-elastic wall properties.CK201

Reactive Flow and Transport Through Complex Systems

The meeting focused on mathematical aspects of reactive flow, diffusion and transport through complex systems. The research interest of the participants varied from physical modeling using PDEs, mathematical modeling using upscaling and homogenization, numerical analysis of PDEs describing reactive transport, PDEs from fluid mechanics, computational methods for random media and computational multiscale methods

International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts

The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days). Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering, industry, and technology, to discuss the development of new mathematical models, theories, and applications that contribute to the advancement of scientific knowledge and practice. Authors proposed research in topics including partial and ordinary differential equations, integer and fractional order equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, probability, computational mathematics, amongst others. The conference was designed to maximize the involvement of all participants and will present the state-of- the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio

Psychological sentiments and economic behavior

This thesis is a contribution to the field of psychology and economics. The two central themes are gift-giving and the effects of rewards. Within these themes, it studies questions like: Why do people donate to charity funds? Why are people sometimes less motivated when they get rewarded for their behavior? Why does the value of a product increase after they have bought it? And why does the market not completely crowd-out gift-giving? Answers to the above and other questions are given by extending economic models with psychological sentiments. The broad message is that taking such sentiments into account often offers insights into why and how institutions should be designed accordingly. Disregarding these effects leads to unintended consequences of incentive schemes.